Hello again. I have a (stupid, but I'm not real sure about the answer-type) question. I'm trying to prove that the second order ODE of the simple pendulum y''=-(g/l)sin y is Lipschitz (using norm 1). After doing some evaluating, I came up with
|u'-v'| + |\frac{g}{l}||\sin u - \sin v|
All I'm...
Hello,
I just have one question that's been bothering me. When I reduce a higher ODE to a First ODE, and if I prove that First ODE satisfies the Lipschitz condition, does that mean that the higher ODE has a unique solution (thanks to some other theorem)?
All clarifications are appreciated...
Well, it is right, however, what I'm really troubled about is how they treated \sum^n_{k=1} |x_k| in the first website (OR \sum^n_{j=1} |x_j| in the second website)
This is what they did after they "split" the summation"
Website 1
\| A \|_1 \leq \max \limits_{\| x\|_1 = 1}...
Yes, this was found on a webpage. I was reading the part for the Derivation of the Matrix 1-norm (column sum norm) on this page.
http://www.maths.lancs.ac.uk/~gilbert/m306a/node6.html
Here, they state that
\| A \|_1 \leq \max \limits_{\| x\|_1 = 1} \sum^n_{i=1} \left|...
Hi guys,
I know this may sound so "newbieish", but I really need some clarification. While resaerching over the net I came across a proof on a derivation of the Matrix p-norms. While reading, I stumbled upon this part of the proof:
\| Ax \|_1 \leq \sum^n_{i=1} \left| \sum^n_{k=1}...
Hello again. I'm kinda stuck trying to prove that the Order of Convergence for the Method of False Position (Regula Falsi) Iteration for finding roots is somewhere between 1 and the golden ratio (approx. 1.62). I do know that
c_k = \frac{f(b_k)a_k - f(a_k)b_k}{f(b_k)-f(a_k)}
Which...
Hello. I've been approached with a problem of explaining why Newton Raphson method fails for some functions. I came across a book in Numerical Analysis (Kellison's book) that the method may fail if
1.) f'(x)=0
2.) The initial value is taken at a maximum or minumum point,
3.) The initial...
I see... that clears things up a bit... so what can you say about Orthodonist's suggestion on getting the order of the rate of convergence (which I know is q in the formula you quoted)? I mean, in the alternative he gave me, he told me to ignore the value of C, but I know that q could be solved...
HallsofIvy:
That's the kind of program I've done so far. I'm finding the roots of
x^2 - 5x - 6
Of course I know the roots (x=-1, x=6) I've already developed the codes for Newton, Secant and Fixed Point Method. I do know that the order of the rate of convergence, q, for each method is q=2...
Thanx so much Orthodonist, your suggestion has helped me very well. However, there's a problem about the rate of convergence that comes out when I test the Secant Method. The Secant Method should give an approximate order of 1.618, but it gives me 1! But anyway, thanks for the help. I will see...
Hello,
Our class was tasked to develop programs for the Fixed Point Method, Newton-Rhapson Method, and the Secant Method, then create a subroutine that could compute the order of the rate of convergence for all the iterative methods. I DO know the orders of rate of convergence of each method...
Hello,
I'm trying to construct a code in determining the Asymptotic Error Constant and the order of the rate of convergence, r for several iterative methods like the Fixed point, Newton Rhapson, and Secant methods in determining roots, using Scilab 4.0 (which is said to behave much like...
so you want to get
f'(z) = \lim_{\Delta z \rightarrow 0} \frac{f(z+\Delta z) - f(z)}{\Delta z}
Express the limit in terms of u(x_0,y_0) and v(x_0,y_0) , that is,x_0, y_0, \Delta x, \Delta y . then evaluate the limit using 2 approaches: when \Delta x = 0 and \Delta y = 0. If f(z) = Arg...